Introduction to Quantum Logic

We present a logical framework that extends the classical binary of $\{T,F\}$ by incorporating superposition, undefined states, entanglement, and contextual dependence. The system generalizes the standard connectives while preserving classical results as a special case, and introduces temporal dynamics to describe the evolution of propositions as flows across a continuum of outcomes. This structure provides a rigorous account of both local and global consistency, offering a tangible mathematical structure for reasoning under indeterminacy. This approach thus bridges classical logic and quantum-inspired models, allowing for more in-depth study of logical systems, epistemology, and the foundations of reasoning.